Ice Puzzle Generator

Demo Link: https://jwang5675.github.io/Ice-Puzzle-Generator/

Background

This repo contains the base code for a simple ice puzzle generator. The goal of the ice puzzle game is to reach the ending destination. The ice puzzle game works by allowing players to move in a single direction until they hit a boulder as if they were sliding on ice. After the player hits a boulder, they will be able to move in another direction.

Motivation and Gameplay: https://www.youtube.com/watch?v=hoCfdfRttT8

Algorithm

Here, I outline the basic algorithm info to generate such ice path puzzles.

Main Algorithm: Input(m, n, difficulty) where (m, n) is the size of the world grid and (difficulty) is a flag denoting how hard the output maze will be.

1. Generate a (m x n) grid that procedurally places boulders on the grid with some defined threshold (t)
2. Generate a random starting point (s) and ending point (e) on the grid
3. Run a modified BFS starting from (s) until it reaches point (e). The modified BFS traverses edges in one direction until a boulder or a wall is reached as a neighboring node.
4. If (e) is unreachable from (s), repeat steps 1 - 3 until a valid map is generated
5. If a valid map generated from (4) satisfies our (difficulty) constraint, output the map. Otherwise, repeats step 1 - 4.

Some important notes to the algorithm:

• Algorithm runs in O(kx) where x = number of grid cells (m * n) and k is the number of tries needed to make a valid map
• Algorithm is technically not deterministic and can run forever and the value of k can be infinite
• However, for small grids (m, n < 20) and a small boulder threshold (threshold < 15%) this should not pose a problem on runtime as there would be many possible solutions and running BFS on a small (20 x 20) grid with a few actual neighbors from traversing edges runs very fast.
• Assuming k is small, the algorithm runs in approximately linear time.

Some example inputs and outputs to the algorithm:

MapGenerator.generateMap(20, 25) can output an easy maze from (s) to (e) with 3 steps: URU

OOOOOOOOOOOOOOOOOOOOOOOeO  
O.......................O  
O.......O..O............O  
O..O....O....O.O........O  
O....O............O...O.O  
O........O.O...O....O...O  
O................OO.....O  
O......................OO  
0.............O........OO  
O..O........O....O...O.OO  
O.............O.......O.O  
O.........O...O..O......O  
O.....................O.O  
O................O..OOOOO  
OO.............O....O...O  
O......O........OO...O..O  
O.O............OO....O.OO  
O.....................O.O  
O..........O...OO.......O  
OOOOsOOOOOOOOOOOOOOOOOOOO  

MapGenerator.generateMap(20, 25) can output a medium maze from (s) to (e) with 11 steps: ULDRURULULU

OOeOOOOOOOOOOOOOOOOOOOOOO  
OO............O..O....O.O  
O.OO.....OO.....O.O.....O  
O...O.O......O.......O..O  
O............O.O........O  
O........O........O..O..O  
O........O...........O..O  
O......OO...............O  
O.......................O  
O.O.O....O...O.O........O  
O..O..O........O....OOO.O  
O.O.....................O  
O.......O..O......O.....O  
O.....OO............O...O  
O...OO..O...O.........O.O  
O.............O...O....OO  
OO.OOO..O...............O  
O.......................O  
O..........OO...........O  
OOOOOOOOOOOOOOOsOOOOOOOOO  

MapGenerator.generateMap(20, 25) can output a hard maze from (s) to (e) with 17 steps: URDLURULDLDLDLDRU

OOeOOOOOOOOOOOOOOOOOOOOOO  
O...........O..OO.......O  
O..O..O..O.O..O.........O  
O...O............OO.....O  
O........O.....O....O...O  
O....O..........O...O.OOO  
O..O..O....O.O..O.....O.O  
OOO...................O.O  
OO.O.O.........O......O.O  
O....O........O...O.....O  
O..O....O....O....O..O..O  
O...................O...O  
O.O..O...O....O.....O...O  
O...........O...........O  
O.O.....OO.........O....O  
OO..................OO..O  
OO..OO....O.....O...O...O  
O...........O.........O.O  
O..OOO..................O  
OOOOOOOOOsOOOOOOOOOOOOOOO  

Rendering

The game is rendered using textures and instanced rendering. Here are the sources for the tilesets that are used within the game:

• Icy Tile: https://bulbapedia.bulbagarden.net/wiki/File:Ice_C.png
• Icy Rock: https://www.reddit.com/r/PixelArt/comments/a3849x/ice_cave_dungeon_tiles_knightsoftartarus/
• End Ladder: https://www.deviantart.com/piacarrot/art/Ice-Path-Tileset-392684771

Gameplay

The game works by having the user select a game difficulty on the main page. Once the difficulty is selected, the game generates a map based on that difficulty and the user must escape the map by moving the player sprite to the ladder.

How difficulty is determined:

• Keep generating mazes and solving them with the above algorithm until we find a maze with a certain amount of minimum steps to complete the maze.
• If a maze requires 3-5 steps to complete, it is an easy maze.
• If a maze requires 6-9 steps to complete, it is a medium maze.
• If a maze requires 10+ steps to complete, it is a hard maze.

Performance Testing

I ran a couple of performance tests on generating different map difficulties. Here are the results of generating (20 x 25) maps:

• Created 10,000 (20 x 25) easy maps, took 5.74 seconds. On average, it takes 0.574 milliseconds to create 1 easy map.
• Created 10,000 (20 x 25) medium maps, took 2.63 seconds. On average, it takes 0.263 milliseconds to create 1 medium map.
• Created 10,000 (20 x 25) hard maps, took 3.36 seconds. On average, it takes 0.336 milliseconds to create 1 hard map.

However, creating large maps increase runtime significantly for easy maps. Here are the results of generating (30 x 35) maps:

• Created 10,000 (30 x 35) easy maps, took 31.42 seconds. On average, it takes 3.142 milliseconds to create 1 easy map.
• Created 10,000 (30 x 35) medium maps, took 6.50 seconds. On average, it takes 0.650 milliseconds to create 1 medium map.
• Created 10,000 (30 x 35) hard maps, took 3.51 seconds. On average, it takes 0.351 milliseconds to create 1 hard map.

Even creating large maps of size 30 x 35, it still takes < 5 milliseconds to create a single map on average.